This is based on the assumption that sugar causes obesity - I don't think there's any strong evidence for that, or that low carb diets work better for fat loss than low fat, from what I've seen both have same effect (calories equated) and both have equally terrible long term adherence/outcomes. Sugar seems like a nice villain but it's more likely that you'd have to tax any high calorie food that tastes good.

And what about physical activity ?